Travel Demand Forecasting: A Fair AI Approach

In recent years, AI methods have been deployed in a broad array of real-world applications due to their outstanding strength in producing highly-accurate predictions. However, there has been a growing recognition that, despite predictive superiority, AI and machine learning techniques have also been accompanied by increasing concerns of fairness [3]. Studies from multiple fields have reported that AI algorithms could be discriminatory to the disadvantaged population groups under various applications, including healthcare, criminal justice, credit assessment, translation, among many others [3, 5, 6, 40, 23, 42]. For example, healthcare systems could underestimate the health condition of black patients than white patients, even if they have the same health risk score [40]. If these inherent biases are not addressed, using these AI systems to assist decision-making will worsen the existing social disparities [39].

Recently, transportation researchers have also started to examine and address the fairness concerns of travel demand forecasting models, e.g., Yan and Howe [51] and Yan and Howe [52]. Specifically, Yan and Howe [51] treated fairness as equal mean per capita travel demand across groups over a period of time and evaluated the fairness issues of several AI methods on demand prediction for ridesourcing services and bike-share systems. Results showed that machine learning spontaneously underestimated the travel demand of disadvantaged people. They also proposed two fairness regularization terms and a corresponding fairness-aware demand prediction model to correct the unfairness. Yan and Howe [52] proposed to use an implicit method, which contains fair representations (i.e., EquiTensors) learned by adversarial learning, to forecast the bike-share demand. These fairness-aware models offer transportation professionals new insights on transportation resource allocations and a novel instrument for designing a fairer transportation ecosystem.

However, there are still two critical knowledge gaps that have yet to be addressed. Firstly, prior research has primarily concentrated on equalizing per capita travel demand among different population groups, but we should note that travel demand disparities may have already been introduced during the data creation process, which is often beyond our control [60, 21]. For example, multiple studies found that rich people are more likely to use ridesourcing services than the poor [53, 58]. That means this behavioral bias among different population groups may naturally exist [41]. However, to date, no study has investigated how to appropriately account for this type of bias, especially for travel demand forecasting models. Second, the existing fairness-aware travel demand forecasting methods necessitate particular model structures, which has very limited adaptability. Thus, developing a model-agnostic (i.e., independent of the model structure) method that can be flexibly adopted by different types of AI models is promising. To date, however, a systematic method in model-agnostic manner to address fairness issues, especially for travel demand forecasting problems, is still lacking.

The goal of travel demand forecasting is to predict the future travel demand for each area (or other spatial unit such as traffic segments) given previously observed time-series data. We consider the transportation network as a weighted directed graph $G=(V,E,\boldsymbol{W})$, where $V$ is a set of nodes (i.e., areas or traffic segments) with $|V|=N$; $E$ is a set of edges representing the connectivity between two nodes; and $\boldsymbol{W}\in\mathbb{R}^{N\times N}$ is a weighted adjacency matrix representing the node’s proximity (e.g., distance or functional similarity). Given weighted directed graph $G$ with $N$ nodes, we assume time $t\in T$ is a discrete variable where $T$ is a set containing all possible timestamps, let $\boldsymbol{x}_{t}=(x_{t}^{i},i\in\mathcal{I})$ represent travel demand at time $t$, where $\mathcal{I}$ is the index set of nodes, $x_{t}^{i}$ is the travel demand corresponding to node $i\in\mathcal{I}$ at time $t$, and let $\boldsymbol{X}_{t}=\left[\boldsymbol{x}_{t-K},\cdots,\boldsymbol{x}_{t-1}\right]$ be historical $K$ travel demand before $\boldsymbol{x}_{t}$. The travel demand forecasting problem could be formulated as learning a function $h(\cdot):\mathbb{R}^{N\times K}\to\mathbb{R}^{N\times M}$ which maps the historical $K$ travel demand to travel demand at next $M$ time interval for all nodes in a given graph $G$. Let $\boldsymbol{\widehat{Y}}_{t}=[\boldsymbol{\widehat{x}}_{t},\cdots,\boldsymbol{\widehat{x}}_{t+M-1}]$ denote the predicted travel demand for next $M$ time interval starting from timestamp $t$, where $\boldsymbol{\widehat{x}}_{t}=(\widehat{x}_{t}^{i},i\in\mathcal{I})$ refers to the predicted travel demand at timestamp $t$ for all nodes, then we can mathematically write:

This study defines Fairness as the equality of prediction accuracy. Intuitively, we assume that the travel demand prediction accuracy should be independent of the protected attributes. Taking racial composition as an example, equality of prediction accuracy suggests that the prediction accuracy for any racial group should be equal. In this study, we use the Absolute Percentage Error (APE) to measure the predictive accuracy instead of the Mean Absolute Error (MAE) or Root Mean Square Error (RMSE). We believe the magnitude of the travel demand (especially for the emerging mobility) for an advantaged community (e.g., high-income community) should be naturally greater than a disadvantaged community [14]. This type of behavioral bias may largely be introduced during the data creation process instead of applying the algorithm [41, 21]. If we quantify the equality of prediction accuracy with MAE and RMSE, which are sensitive to the magnitude of the forecasting outcome, machine learning may replicate, or even reinforce and potentially exacerbate existing biases. Instead, APE scales the magnitude and cancels out the behavioral bias that has already been embedded in the data.

Recall from the previous section, a travel demand forecasting model is to learn a function $h$ which takes $K$ historical travel demands $\left[\boldsymbol{x}_{t-K},\cdots,\boldsymbol{x}_{t-1}\right]$ as input and predict travel demands from next $M$ time interval starting from time $t$, i.e., $\boldsymbol{Y}_{t}$. We define $\boldsymbol{e}_{t}=(e_{t}^{i},i\in\mathcal{I})$ to indicate the prediction accuracy (i.e., APE) at time $t$, and $e_{t}^{i}$ is the prediction accuracy of node $i$ at time $t$. Specifically,

Suppose $\boldsymbol{Z}=[\boldsymbol{z}_{j},j\in\mathcal{J}]$ is the matrix of protected attributes of interest, where $\mathcal{J}=\{1,2,\ldots,Q\}$ is the index set of attributes, where $Q$ is the total number of protected attributes; $\boldsymbol{z}_{j}=(z_{j}^{i},i\in\mathcal{I})$ represents the protected attribute $j$, and $z_{j}^{i}$ denotes the protected attribute $j$ at node $i$, $\mathcal{I}$ is the set of index for nodes. Denote $p_{j}^{i}$ as a binary indicator indicating if node $i$ is belonging to advantaged (i.e., $p_{j}^{i}=1$) or disadvantaged (i.e., $p_{j}^{i}=0$) groups for protected attribute $j$, and accordingly let $\mathcal{I}_{j}^{+}=\{i:p_{j}^{i}=1\}$ and $\mathcal{I}_{j}^{-}=\{i:p_{j}^{i}=0\}$ represent the set of advantaged and disadvantaged node index for demographic attribute $j$ with size $N_{j}^{+}=|\mathcal{I}_{j}^{+}|$ and $N_{j}^{-}=|\mathcal{I}_{j}^{-}|$, respectively. We note that assigning value for $p_{j}^{i}$, i.e., determining whether each node should be labeled as advantaged or disadvantaged, is context-specific. This determination could be guided by the criteria or statistics defined by local government [51]. Subsequently, Equality of Prediction Accuracy is defined as:

In this study, we introduce Prediction Accuracy Gap (PAG) as a fairness metric to measure prediction accuracy disparity and if fairness/unfairness achieves/occurs. Define:

Intuitively speaking, PAG directly measures the prediction accuracy disparity between these two types of nodes. A high value of PAG indicates that the machine learning model delivers inconsistent predictive performance among nodes; in most cases, the performance is worse in disadvantaged nodes.

In this study, we also use Correlation Coefficient as another fairness metric. The correlation coefficient can naturally measure the extent to which the predictions are biased on specific protected groups. Intuitively, if fairness is achieved, correlation between prediction accuracy and any protected attribute should be zero. By using correlation coefficient as a measure of fairness, we assume that the target variable (i.e., prediction accuracy) is linearly correlated with the independent variable (i.e., protected attribute).

Recall from the discussions above, $\boldsymbol{e}_{t}$ is the prediction accuracy (APE) at time $t$, and $\boldsymbol{z}_{t}$ refers to the protected attribute $j$ for all nodes. Then, the correlation between prediction accuracy $\boldsymbol{e}_{t}$ and the protected attribute $\boldsymbol{z}_{j}$ across all nodes is denoted by $r(\boldsymbol{e}_{t},\boldsymbol{z}_{j})$. Define:

In this study, we introduce an absolute correlation regularization approach, which adapts the efforts from Beutel et al. [9], to mitigate the prediction accuracy disparities existing among groups. In Beutel et al. [9], the authors applied this approach to a classification problem by minimizing the false positive rate (FPR) gap between groups. We generalize this approach to a regression setting (i.e., travel demand forecasting problem) by minimizing the prediction accuracy disparities among different communities.

More importantly, including Beutel et al. [9], most previous studies have primarily focused on correcting the unfairness of one single attribute. In real-world dataset, however, the debiased model and results could differ among various protected attributes. Also, a model that is fair for one protected attribute could still be unfair for other attributes [46, 60]. One feasible solution to solve this issue is to consider multiple attributes at the same time when correcting the unfairness of the models. We expected that a fair model should produce fair predictions for all types of attributes instead of focusing solely on one.

Therefore, we propose a methodology that can correct the unfairness for multiple protected attributes. More specifically, we propose to use the Multiple Correlation Coefficient [4], denoted as $R$, to measure the correlation between the target variable, i.e., prediction accuracy, and a set of protected attributes (including race, education, age and income). A larger $R$ suggests that a stronger dependence may exist between the target variable and the explanatory variables. We expect that a fair prediction should lead to $R=0$, or at least, a small value. Accordingly, we will use $R$ as the regularization term in the loss function to account for fairness loss. We should note that the linear model may encounter potential multicollinearity concerns. However, there is no need to address them since the goal of the linear model is forecasting rather than estimating the coefficients [45].

Recall from previous subsections, we will use the prediction accuracy $\boldsymbol{e}_{t}$ as the target variable and $\boldsymbol{Z}=[\boldsymbol{z}_{j},j\in\mathcal{J}]$ to represent the matrix of multiple protected attributes of interest. And, we use $r(\boldsymbol{e}_{t},\boldsymbol{z}_{j})$ to indicate the correlation between prediction accuracy $\boldsymbol{e}_{t}$ and the protected attribute $\boldsymbol{z}_{j}$ across all nodes. Given these notations, we will naturally write the vector of correlations between each protected attribute $\boldsymbol{z}_{j}$ and prediction accuracy $\boldsymbol{e}_{j}$, i.e., $\boldsymbol{c}=\left(r(\boldsymbol{e}_{t},\boldsymbol{z}_{1}),r(\boldsymbol{e}_{t},\boldsymbol{z}_{2}),\ldots,r(\boldsymbol{e}_{t},\boldsymbol{z}_{Q})\right)^{\top}$, and the correlation matrix calculated by the correlation coefficient among each pair of protected attributes, denoted as $\mathbf{\Omega}$, i.e.,

Consequently, the multiple correlation coefficient between $\boldsymbol{e}_{t}$ and $\mathbf{Z}$), i.e., $R(\boldsymbol{e}_{t},\mathbf{Z})$, which is the square root of the coefficient of determination (i.e., $R^{2}$) of the linear model [2], can be written as:

Accordingly, given graph $G$ and a forecasting model $\boldsymbol{\widehat{Y}}_{t}=h(\boldsymbol{X}_{t}|G)$, we add the multiple correlation coefficient, $R$, into the loss function, denoted as $L(\boldsymbol{X}_{t},\mathbf{Z}|G)$ as shown in Eq. 5. In this way, the model will simultaneously account for the unfairness issues sourcing from multiple protected attributes. Let $\boldsymbol{Y}_{t}=[\boldsymbol{x}_{t},\cdots,\boldsymbol{x}_{t+M-1}]$ denote the ground truth travel demand of next $M$ time intervals starting from $t$, mathematically, the loss function of the forecasting model to be minimized, i.e., $L(\boldsymbol{X}_{t},\mathbf{Z}|G)$, is written as:

Note that when there is only one single protected attribute of interest, the multiple correlation coefficient, i.e., Eq. 4 reduces to Eq. 3.

In this study, we collected the publicly available ridesourcing-trip data from Chicago Data Portal¹¹1https://data.cityofchicago.org/Transportation/Transportation-Network-Providers-Trips-2018-2022-/m6dm-c72p/explore for case study. The data are from November 1, 2018 to March 31, 2019, containing 45,338,599 trips. There are plenty of attributes included in this dataset, but only pick-up locations and timestamps are considered for this research. Since we focused on trip generation (i.e., origin demand) forecasting, all trips are aggregated at the census-tract level and hourly counted. We prepared the data for modeling in the same way as previous studies [58], to account for the missing-data issues and outliers. The data preparation process produced the trip generation data for 711 census tracts. We split the first 70% data for training, the following 10% for validation and the remaining for testing. The census-tract-level demographic data (i.e., protected attributes) were collected from the American Community Survey 2013–2017 5-year estimates data, including the percentage of white, the percentage of low-income households, the percentage of population with a bachelor’s degree or above and the percentage of young populations (with age in 18-44).

This study also collected ridesourcing-trip data from RideAustin²²2https://data.world/ride-austin/ride-austin-june-6-april-13 for case study. The data ranges from October 1, 2016 to April 13, 2017, including 1,259,574 trips in total. Similar to the case study in Chicago, we only retained pick-up locations and the corresponding timestamps from the dataset for empirical analysis. All ridesourcing trips were aggregated at the census-tract level on an hourly basis. Finally, the prepared dataset includes 191 census tracts. The first 70% of the whole dataset was split for model training, followed by the following 10% for validation and 20% for testing. Four protected attributes, including the percentage of white, the percentage of low-income households, the percentage of population with a bachelor’s degree or above and the percentage of young populations (aged 18-44) were also collected from American Community Survey 2013–2017 5-year estimates data.

In this study, we applied seven models as the major baseline models to measure the fairness metrics and perform the bias mitigation. We also compared their performance with historical average method. All used models are detailed as follows:

• 1.

  Historical Average (HA): We calculate the historical average travel demand using the mean values of all observations from the inputted sequence.

• 2.

  Multivariate Linear Regression (MLR): MLR is frequently used in machine learning studies as the benchmark model. This study treats observations at every timestamp $t$ as a covariate.

• 3.

  Autoregressive Integrated Moving Average Model (ARIMA): ARIMA is one of the most fundamental statistical models for forecasting time-series data [38]. ARIMA consists of three basic parts: auto-regressive, first-differencing and moving-average part. The order of the auto-regressive ($p$) and moving-average ($q$) and the degree of first-differencing ($d$) included should be prespecified before building the model. In this study, we established ARIMA model to predict the travel demand for all areas at once.

• 4.

  Multiple Layer Perception (MLP): MLP is a commonly-used deep neural net model. In this study, the model architecture is set as 1 hidden layer with 300 hidden linear neurons. A drop-out layer rate 0.01 is set after the hidden layer to avoid overfitting.

• 5.

  Gated Recurrent Unit (GRU): GRU is a widely-adopted Recurrent Neural Network (RNN) model with gated hidden neurons [20]. GRU can generate the predicted travel demand $x_{i,t+1}$ by inputting the hidden status at timesampe $t-1$ and the travel demand at timestamp $x_{i,t}$. In this way, GRU can dynamically capture the travel demand information at the current timestamp while maintaining the historical demand trend. We use GRU model for forecasting the travel demand for all nodes at once.

• 6.

  Temporal Graph Convolution Network (T-GCN): T-GCN can capture the spatial dependency and temporal information at the same time [59]. Specifically, the spatial dependency is calibrated by the spatial adjacency graph $G_{adj}$, where 1 indicates two nodes are spatially adjacent and 0 otherwise. T-GCN takes the hidden status at timestamp $t-1$ and the graph-convolution-processed travel demand information at timestamp $t$ as the input. Therefore, T-GCN can effectively deal with data that have strong spatial dependency such traffic speed data.

• 7.

  Convolutional Long-short Term Memory (ConvLSTM): ConvLSTM is one of the most novel approaches for spatio-temporal forecasting problem [44]. ConvLSTM has a convolution structure in both the input-to-state and state-to-state transitions; it determines a certain cell’s future states by considering the inputs and past states from its local neighbors. This characteristic allows it a more powerful strength in handling spatio-temporal correlations. In this study, the convolutional kernel size of the ConvLSTM is set to 5.

• 8.

  Spatio-Temporal Graph Convolution Network (STGCN): STGCN is an effective approach for spatio-temporal traffic flow forecasting [57]. STGCN consists of several spatio-temporal convolution (ST-Conv) blocks. Each block has a “sandwich”-like structure: two gated sequential convolution layers and one spatial graph convolution layer in between. This allows STGCN to distill the most useful spatial features and capture the most essential temporal features collectively. In this study, we set the number of ST-Conv blocks as 2. Let $d_{i,j}$ denote the distance between node $i$ and node $j$, the element in the weighted adjacency matrix, i.e., $w_{i,j}\in\boldsymbol{W}$, is given by:

  $$w_{i,j}=\begin{cases}\exp\left(-\frac{d_{ij}^{2}}{\sigma^{2}}\right),&i\neq j\text{ and }\exp\left(-\frac{d_{ij}^{2}}{\sigma^{2}}\right)\geq\alpha\\ 0,&\text{ otherwise. }\end{cases},$$

  (7)

  where $\sigma^{2}$ and $\alpha$, assigned as $10^{4}$ and $0.5$, are thresholds that control the sparsity of $\boldsymbol{W}$.

The predictive performance and two fairness metrics (i.e., correlation [Corr] and prediction accuracy gap [PAG]) of all models with respect to four protected attributes are presented in Table 3 and Table 4.

We show the results of the predictive performance for each benchmark in Chicago ridesourcing-trip data (Table 3) and Austin ridesourcing-trip data (Table 4).

Regarding prediction accuracy, all benchmark models show a similar trend across two case studies. The performance ranking is ConvLSTM $\approx$ STGCN $>$ GRU $>$ T-GCN $>$ MLP $>$ ARIMA $>$ HA. It indicates that the prediction accuracy gradually increases as the model becomes more complex. Two convolution models, i.e., STGCN and CovLSTM, are best-performing among all models. Both STGCN and ConvLSTM can incorporate spatial and temporal information through the convolution blocks, which enhance their prediction power. Among two RNN-based models, GRU outperformed T-GCN for both MAE and RMSE. MLP, due to its simple model architecture, underperformed all neural network-based models. Compared with deep neural networks, traditional statistical models, i.e., MLR and ARIMA, have relatively low prediction accuracy. However, their performance still significantly outperformed HA. MLR and ARIMA both have a prespecified (linear) model structure and cannot capture the nonlinearity between the inputs and target variables, which restricts the predictive capability.

Regarding fairness issues, for Chicago ridesourcing-trip data, Table 3 shows that HA exhibits completely inverse relationships in correlation and gap compared with other models. Since HA has the worst predictive performance, the corresponding fairness metrics could be unreliable. The results illustrate that both statistical and deep learning models have evident fairness issues. protected attributes, including race, education and age, are negatively correlated with the prediction accuracy which means that communities with high proportion of white population, high education-attainment rate and more young people have high prediction accuracy. Income level is positively related to predictive performance, indicating that communities with more low-income households may have higher perdition error. In terms of magnitude, we found that education and age have the largest value of correlation with prediction accuracy, followed by income and race. Although there are variations in the magnitude of correlations, the signs for all protected attributes among all models except for HA are consistent. In addition to correlations, we also explored the PAG between the advantaged groups and disadvantaged groups. Table 3 presents that all gaps have a positive value (except for HA), indicating that the prediction error for minority groups is higher than for advantaged groups. Additionally, the prediction accuracy disparity is more pronounced for education and age than for race and income.

For Austin ridesourcing-trip data, all benchmark models demonstrate a similar performance (both trend and direction of associations) compared with using Chicago dataset. However, results showed that the fairness issues are relatively subdued in Austin dataset. In other words, the extent of unfairness (as shown by correlation coefficient and PAG) is notably diminished in comparison to the Chicago dataset. Notably, Table 4 shows that prediction accuracy is less biased regarding race and income. Two best-performing models (i.e., STGCN and ConvLSTM) may produce satisfying fair predictions. For example, the correlation between prediction accuracy and race delivered by ConvLSTM is 0.000 and the PAG regarding race is only -0.391%. This evidence indicates that the unfairness in prediction accuracy should be of little concern for this protected attribute.

We tuned a set of values of $\lambda$ (i.e., the weight for fairness loss) by grid search to validate the effectiveness of the proposed unfairness correction method. Table 5 and Table 6 present the results of simultaneously mitigating the unfairness issues for multiple protected attributes across two case studies. We only present the best $\lambda$ (i.e., the one that can significantly improve fairness while largely preserving prediction accuracy) from the empirical experiments. We also add experimental results of correcting unfairness of only one single attribute at the bottom of each table for comparison. For the sensitivity analysis of $\lambda$, please refer to Section 5.3. As discussed in previous section, only very limited prediction accuracy disparities are detected on race (percentage of white population) and income (percentage of low-income households) in the case study of Austin (as shown in Table 4). Thus, we decided to only correct the unfairness of prediction accuracy manifested in education (percentage of bachelor holders) and age (percentage of young population) in this case.

There are several key findings to highlight. First, results of the multi-attribute scenario show great consistency across two datasets. Table 5 and Table 6 show that in almost all trails, incorporating a small fairness weight can significantly reduce the absolute value of the correlation and PAG across all protected attributes. For example, in Chicago dataset, incorporating only 0.050 fairness weight for GRU can lead to 85.142%, 86.386%, 92.004%, 94.927% reduction of the absolute values of the PAG for race, education, age and income, respectively. In the meantime, the correlation between prediction accuracy and protected attributes also improved more than 60%, but RMSE only increased by 2.062%. In Austin dataset, setting $\lambda$ as 0.025 for ConvLSTM yields 68.973% and 88.496% PAG shrinkage on education and age by sacrificing only 5.661% increase on RMSE (from 3.162 to 3.341).

Second, the effects of the proposed unfariness correction method varies across models and protected attributes. For example, Table 5 shows that when mitigating the income bias, setting $\lambda$ as 0.025 only reduces 54.923% of the PAG in absolute value for STGCN; while for ConvLSTM, the same setting can lead to a 95.081% reduction. In addition, the case study on Chicago ridesourcing-trip data reveals that compared with education and age, the absolute value of PAG for race and income are more likely to be largely reduced (i.e., to less than 1%).

Third, by choosing an appropriate $\lambda$, both fairness and accuracy can be improved at the same time. Taking Chicago dataset as an example, adding 0.025 fairness weight on STGCN can simultaneously reduce the absolute value of PAG and correlations for all protected attributes while even reducing RMSE by 1.347%.

Moreover, we found that MLR and ARIMA showed limited capabilities in mitigating unfairness. In Chicago dataset, the prediction accuracy disparities of education and age (as shown in the change of PAG) for MLR and ARIMA even increased after debiasing multiple protected attributes. Also, our examination of the Austin dataset indicated that after incorporating the proposed fairness regularization term, although the PAG for MLR and ARIMA decreased, the magnitude of this reduction was comparatively modest in comparison to other models. In fact, these two models are less flexible compared with other deep learning models since they have a pre-specified model structure. We believe that this inherent limitation could hinder their effectiveness in addressing fairness concerns.

Lastly, in most cases, our proposed multi-attribute unfairness correction method shows better performance in reducing disparities of prediction and preserving fairness compared with only debiasing a single attribute, especially for more complex deep learning models (e.g., GRU, T-GCN, STGCN and ConvLSTM). For example, Table 5 shows that when considering multiple attributes together, GRU and ConvLSTM can close more than 94% of PAG of income in absolute value; while for the single-attribute scenario, the PAG is only reduced by around 60%. However, we also observed in certain cases, single-attribute unfairness correction could produce fairer performance. For example, GRU is found to be more effective in reducing PAG when only debiasing age for Austin dataset.

To provide a more comprehensive demonstration of the efficacy of the proposed multi-attribute unfairness correction approach and to pinpoint potential shortcomings in the single-attribute bias correction method, we conduct a comparative analysis of unfairness correction outcomes achieved through debiasing the age variable alone versus debiasing multiple attributes simultaneously. We have chosen the top-performing model, i.e., ConvLSTM, for demonstration. The resulting findings can be found in Table 7.

We found that correcting unfairness regarding one attribute might even create more biases for other protected attributes, which aligns with one previous study [60]. This finding highlights the importance of considering multiple protected attributes at once. Specifically, results showed that compared with the original model that purely focused on prediction accuracy, solely correcting unfairness of age variable could indeed help drop the absolute value of PAG. However, by only considering age, the PAG for other variables, especially for race and income variables, even increases. For example, in Austin dataset, debiasing only Age shrank the PAG from 4.642% to 0.771% by significantly sacrificing the PAG of income from 0.888% to 8.238%. This unexpected outcome may further shed light on the fact that the transportation resource allocations intended to be fair for distinct age groups could nonetheless still be unfair regarding communities with different income levels. Notably, the results showed that the proposed multi-attribute unfairness correction method can effectively debias multiple protected attributes and in almost all cases the absolute value of PAG is significantly dropped compared with the original model without sacrificing too much prediction accuracy.

We also explored the influence of the fairness weight, i.e., $\lambda$, in shaping the interaction between accuracy and fairness based on the predictive performance of seven models with four protected attributes. Fig. 1 presented in C illustrates the sensitivity analysis of $\lambda$ in determining accuracy and fairness. The $x$-axis is the value of $\lambda$ while the $y$-axis is the performance metrics (RMSE, correlation coefficient and PAG). Generally, the accuracy for all models decreases when $\lambda$ gradually increases. In terms of RMSE, the marginal effect of $\lambda$ on more complex models is relatively small. Figures show that as $\lambda$ grows, the correlation will first drastically increase/decrease, and then remain flat. Notably, setting a small weight ($\lambda\leq 0.1$) can lead the correlation drop to around 0. The PAG shows a decreasing trend as $\lambda$ gradually increases. But in most cases, the gap may get over-corrected when $\lambda$ is greater than 0.1. According to the tables shown in Section 5.2, a suitable fairness weight possibly exists in the range between 0 to 0.1. This finding further reinforces the effectiveness of our proposed unfairness correction approach: incorporating only a small amount of weight for fairness can lead to a significant improvement in producing fair predictions. We also found that increasing fairness weight may not monotonically reduce the PAG. This finding echoes the results in Zheng et al. [60], where they showed that increasing fairness weight might even extend the PAG. Our computational experiments show that this scenario frequently occurs for traditional statistical models. This finding also suggests the need for more fine-grained searching ranges of $\lambda$ when conducting hyperparameter tuning. Overall, the sensitivity of the effects of $\lambda$ shows great consistency across two case studies. Finally, we noticed that in Austin case, setting fairness weight as 0.4 for GRU led a substantial increase in RMSE and PAG. One possible reason could be that this combination of hyperparameters might explode the gradients and thus lead to this numerical instability.

This study compares the performance of the proposed unfairness correction approach (i.e., the absolute correlation regularization term) with three state-of-the-art benchmark regularizers, including Equal Mean (EM) [16], Region-based Fairness Gap (RFG) and Individual-based Fairness Gap (IFG) [51]. For experiments, we only consider single-attribute scenario as these three benchmark regularizers are explicitly designed for addressing unfairness of a single protected attribute. For Chicago Ridesourcing dataset, we select race (percentage of white population) for model debiasing; while for RideAustin dataset, education variable (percentage of bachelor holders) is chosen for comparison. All benchmark regularizers are set with the best-performing $\lambda$ yielded by our proposed method for comparison.

Table 8 presents the comparative analysis between our proposed method (i.e., absolute correlation regularizer) and three state-of-the-art benchmark regularizers. Results unequivocally show that the proposed method evidently outperforms other methods in terms of preserving prediction accuracy as well as improving fairness. Among all regularizers, EM delivers the worst performance. This is expected since EM focuses on balancing the target variable (i.e., ridesourcing demand) of disadvantaged and advantaged groups instead of the prediction accuracy. However, this method could be questionable since the variations in ridesourcing usage between different population groups may naturally exist due to socioeconomic and demographic disparities [14]. RFG and IFG tend to yield improved outcomes in terms of both accuracy and fairness when compared to EM. Moreover, in certain scenarios, their performance (especially for correlation and RMSE) surpasses that of the proposed method. We attribute this to their capabilities to effectively reduce variations in per capita travel demand for each individual population group, as indicated in Yan and Howe [51]. However, these two metrics may still not be able to fully account for the inherent disparities of different population groups in generating travel demand [58]. In most cases, especially for deep learning models with more complex model architectures, the proposed method can significantly help reduce the PAG between disadvantaged and advantaged groups while keeping the prediction error lowest. Although in some cases the proposed method may not be the best-performing one regarding accuracy, the produced RMSE still remains within an acceptable range.

The merit of the proposed unfairness correction method is threefold.

First, a new regularizer to simultaneously debias multiple protected attributes. The current literature rarely discusses how to effectively address fairness issues for multiple protected attributes. However, designing a method that can accommodate various fairness needs is necessary for real-world applications [46]. This study addresses this issue by proposing to use Multiple Correlation Coefficient (i.e., $R$ of a linear model) as a regularization term and incorporating it into the loss function. The multiple correlation coefficient can directly measure the correlation between the target variable (i.e., prediction accuracy) and a set of protected demographic variables (i.e., race, age, education and income). By minimizing the coefficient of multiple correlation, AI models can simultaneously debias multiple sensitive attributes. Unlike adding multiple regularization terms (one for each attribute) [51], this approach is straightforward and easy to implement, and there is no need to fine-tune the fairness weight for different attributes (only one is enough). Also, this approach has little concern about the multicolinearity (as shown in Appendix.B) issues among different protected attributes, since the goal of the linear model is to use the set of protected attributes to forecast the prediction errors instead of estimating and interpreting the beta coefficients [45]. Overall, our proposed unfairness correction method enables future studies to flexibly debias both single or multiple protected attributes of interests.

Second, flexibility and transparency. The proposed unfairness correction method is model-agnostic and may be generalizable for different applications and different data modalities. We implemented the unfairness correction method on both statistical and deep learning models. Results jointly demonstrated that, generally, this approach could mitigate the unfairness while only slightly reducing the overall accuracy. Specifically, we correct the unfairness by incorporating an explicitly designed absolute correlation regularization term into the loss function without modifying the model structure. It allows the unfairness correction method great flexibility to be independent of the underlying model. Scholars can thus flexibly adopt any model they want in addressing fairness issues. Also, the proposed method enjoys great transparency since end-users (e.g., stakeholders) can easily understand how fairness is being taken into account and improved (from the fairness regularization term). Moreover, this method is transferable for other forecasting applications. Besides travel demand forecasting, other important issues including traffic count forecasting, pedestrian activity forecasting or crash frequency forecasting may also have silent fairness problems. Researchers can apply our proposed method to address the fairness issues and provide fair decision-making. This study only examined the proposed method using time-series (panel) data. However, we believe it can be easily generalized to other applications with different data modality. For example, transportation-planning models, which usually use cross-sectional data, should also be examined with fairness analysis. Our unfairness correction method can be flexibly adopted by planning models [e.g. 58] to inform fair design of transportation ecosystems. Flexibility is also reflected in that, once the models are trained, access to protected attributes is no longer required. Unlike the post-processing technique that always requires access to the protected attribute [27, 1], our approach lifts this restriction and can be flexibly adapted for future forecasting tasks.

Third, effectiveness in achieving fairness while preserving prediction accuracy. Multiple studies reported that machine learning has a trade-off between accuracy and fairness (e.g., [8, 1]), i.e., the reduction of unfairness will inevitably trigger an accuracy drop. Our scheme addresses this trade-off by incorporating an interactive weight coefficient (i.e., $\lambda$) into the loss function. We treat $\lambda$ as a hyperparameter of the learning task and tune it together with other hyperparameters. In this way, the model automatically finds the optimal hyperparameter combination that has the best performance in improving fairness while maintaining prediction accuracy. Most of our experiments revealed that this approach could significantly reduce unfairness only at little expense of accuracy decline. While in some cases, our proposed method can even significantly improve fairness and slightly improve prediction accuracy.

Dynamically balancing the supply and demand for transportation systems is important to improve cost-benefit effects and efficiency. And this balance relies heavily on accurate predictions [22]. Although machine learning intensively promotes predictions, it may simultaneously introduce bias. The overall satisfactory predictions may hide a huge prediction accuracy gap across areas of the city or underrepresented groups of residents [51, 60]. Our study also confirms this finding. Specifically, Table 3 shows that both machine learning and statistical models can produce lower prediction accuracy for the disadvantaged communities (i.e., the non-white-majority, the lower-education-attainment, the elderly and the low-income) than that of the advantaged communities. The predictive disparity implies that if transportation planners naively use such travel demand forecasting models without accounting for the fairness issues, the modeling results will lead to ineffective transportation resource allocations, impede the mobility of the disadvantaged communities, and even possibly further exacerbate the existing operational biases of ridesourcing services, e.g., higher trip-cancellation rate, longer waiting times and higher per-mile fees for disadvantaged communities [12, 55, 11, 13].

Our proposed method can help mitigate the unfairness issues of the current ridesourcing operations to better serve the disadvantaged communities. We believe that ridesourcing policymakers should consider incorporating our proposed method into the travel demand modeling framework to inform fairer ridesourcing resource allocations and operations. Additionally, two fairness metrics can be used by city governments to evaluate and regulate ridesourcing operations. Moreover, the fairness measurements and unfairness correction method can be adopted to facilitate the effective operations of other travel modes such as public transit and shared micromobility. For example, an accurate and fair demand forecasting model will enable transit authorities to provide more personalized transit services to balance operation efficiency and effectiveness [26]. Also, a fairness-aware travel demand forecasting model will help micromobility (e.g., bikeshare and e-scooter) operators better rebalance the vehicles and ensure fair distribution of service availability throughout the day [54].

This study has some limitations that warrant follow-up investigations. For example, we only evaluated the proposed methodology using two fairness metrics (i.e., prediction accuracy gap and correlation coefficient) in this paper. Future works may consider using a wider range of fairness metrics to conduct a comprehensive evaluation. Moreover, by using correlation techniques, we assume the prediction accuracy is linearly correlated with the protected attributes. Future studies may consider exploring whether this association is nonlinear and developing corresponding methods. Another widely debated research topic is the connection between accuracy and fairness. Several previous studies have shown that the accuracy-fairness trade-off exists across datasets and applications [8, 21] while others have shown that improvements in accuracy and fairness can co-occur [50]. Hence, forthcoming investigations may shed further light on this relationship, such as identifying scenarios in which fairness and accuracy can both be enhanced or where the accuracy-fairness trade-off is prominent. Finally, this study only examined one travel mode (i.e., ridesourcing). A more comprehensive analysis that includes various travel modes (e.g., transit, car-sharing, and shared micromobility) and diverse contexts (e.g., different locations) should be conducted to test the generalizability and robustness of the unfairness correction method.